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Boundary conditions for the numerical solution of elliptic equations in exterior regionsElliptic equations in exterior regions frequently require a boundary condition at infinity to ensure the well-posedness of the problem. Examples of practical applications include the Helmholtz equation and Laplace's equation. Computational procedures based on a direct discretization of the elliptic problem require the replacement of the condition on a finite artificial surface. Direct imposition of the condition at infinity along the finite boundary results in large errors. A sequence of boundary conditions is developed which provides increasingly accurate approximations to the problem in the infinite domain. Estimates of the error due to the finite boundary are obtained for several cases. Computations are presented which demonstrate the increased accuracy that can be obtained by the use of the higher order boundary conditions. The examples are based on a finite element formulation but finite difference methods can also be used.
Document ID
19800015552
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Bayliss, A.
(NASA Langley Research Center Hampton, VA, United States)
Gunzburger, M.
(Tennessee Univ.)
Turkel, E.
(New York Univ.)
Date Acquired
September 4, 2013
Publication Date
January 1, 1980
Subject Category
Numerical Analysis
Report/Patent Number
NASA-CR-153185
REPT-80-1
Accession Number
80N24044
Funding Number(s)
CONTRACT_GRANT: DAAG29-78-C-0024
CONTRACT_GRANT: EY-76-C-02-3077
CONTRACT_GRANT: NAS1-14101
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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